Analytic Methods for Diophantine Equations and Diophantine Inequalities

Name: Analytic Methods for Diophantine Equations and Diophantine Inequalities
Price: 64.73 USD
Availability: InStock
ISBN: 9780521605830

ISBN-10: 0521605830

ISBN-13: 9780521605830

Edition: 2nd 2004

Authors: Harold Davenport, T. D. Browning

List price: $62.99

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Description:

Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities.…

Book details

List price: $62.99
Edition: 2nd
Copyright year: 2004
Publisher: Cambridge University Press
Publication date: 2/7/2005
Binding: Paperback
Pages: 160
Size: 5.91" wide x 8.98" long x 0.51" tall
Weight: 0.550
Language: English

Harold Davenport F.R.S. was the late Rouse Ball Professor of Mathematics at the University of Cambridge and Fellow of Trinity College.



Preface


Foreword



Introduction



Waringï¿½s problem: history



Weylï¿½s inequality and Huaï¿½s inequality



Waringï¿½s problem: the asymptotic formula



Waringï¿½s problem: the singular series



The singular series continued



The equation C1xk1 +ï¿½+ Csxks=N



The equation C1xk1 +ï¿½+ Csxks=0



Waringï¿½s problem: the number G (k)



The equation C1xk1 +ï¿½+ Csxks=0 again



General homoogeneous equations: Birchï¿½s theorem



The geometry of numbers



cubic forms



Cubic forms: bilinear equations



Cubic forms: minor arcs and major arcs



Cubic forms: the singular integral



Cubic forms: the singular series



Cubic forms: the p-adic problem



Homogeneous equations of higher degree



A Diophantine inequality


Bibliography


Index